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2 ANGLEFrom division of the circle, all of angular measurement is derived and provableAngle deal with direction – not spaceAngle is a relationship between two linesWe can measure this relationship if we extend the lines until they intersectThe intersection is called the vertex, and the lines are sidesSee figure 7.1

3 Figure 7.1The angle is defined as AOB. It refers to the directions of the sides, not to the space between them

4 Angle (cont’) Right angle – one-fourth of circle or one quadrantAcute angle - an angle measures less than 90oObtuse angle - an angel measure more than 90oSee figure 7.2

5 A right angle is 90.if smaller, it is acute; if larger, it is obtuseFigure 7.2A right angle is 90.if smaller, it is acute; if larger, it is obtuse

6 The level One of the most useful measurement instruments is the levelThese ‘bubble instrument’ are widely use in engineering metrologyFor precision measurementPrecision levelsClinometersTheodolitesUse in the shop (less precision measurement)Bench levelMechanic’s levelAll of these instruments use bubbles in fluid filled tubes

7 The longer the radius of curvature, the more precise the level will beFigure 7.4The longer the radius of curvature, the more precise the level will be

10 Reading levelFigure 7.7: the readings are the number of divisions that the bubble moves

11 Level adjustmentFirst, orient the level on the surface until the bubble is centeredThen clamp the straightedge to the surface along one side of the levelReverse the level and read the errorRepeat this process, orienting to a new location on the surface until you have achieved the desired accuracy* If the level is so far out of calibration that the bubble is off the scale, it may take long and tedious adjustment to make it usable again.

13 Clinometer The block level is restricted to relatively small anglesThis restriction is removed in the clinometerIt is a level mounted in a frame so that the frame may be turned at any desired angle to the horizontal reference

14 A few of many types of clinometersFigure 7.8A few of many types of clinometers

15 Measuring with clinometerPlace the base against the surface with the circle clamp in the free positionRotate the level until it is approximately levelClamp the circle, then use the fine adjustment to center the bubbleTurn the micrometer knob first until you have a reading on the degree scale in line with the fiducial arrowheadAdd the reading on the top scale to the degree scaleIn clinometer, you read the bubble only to provide reference plane; you must read the angle from another scale

16 Disadvantage of levelsThere are four principal disadvantage of levelsGeneral ignorance about their proper use and applicationThe time required to settle downTheir single sensitivity characteristicThey do not produce any output that can be used as loading for a measurement system

17 THE PROTRACTORFor measuring angles, the simple protractor is equivalent to the rule for measuring lengthLike a steel rule, the simple protractor has limited use.But mechanical additions to the rule resulted in the versatile combination square (e.g: vernier caliper & height gage)We make similar modifications on the simple protractor, we get universal bevel protractorFigure 7.9

19 Degrees are read directly, but minutes are read with the vernier scaleFigure 7.10Degrees are read directly, but minutes are read with the vernier scaleCare must be used to read the minutes from the correct pair of lined-up graduation12o 50’

20 Figure 7.11Always read the vernier in the same direction from zero that the dial is read and add the vernier minutes to the scale degrees

21 Application for vernier protractorWe can determine the angle or degrees in any arc with the universal bevel protractorWhen protractor is set at 90, (figure 7.12B), all four angles are as readIf you turn the blade counterclockwise (figure 7.12A) which happens in two position as shown.If you turn the blade clockwise (figure 7.12C), the angle read will be formed only in two places, which are always from the blade to the base rotating clockwise

22 Figure 7.12 & 7.13Figure 7.12: When reading from 90, these are positions where the angle and its supplement are foundFigure 7.13: when reading from 0, there is little danger of confusing the angle and its supplement

24 TRIGONOMETRIC FUNCTIONSThe trigonometric functions, formed by the sides of trianglesFor elementary angle computation, we simply use the natural functionsSineCosineTangent

25 Sine bars and plateThe sine bar, a steel bar that has a cylinder near each end, forms a hypotenuseThe instrument is designed with a distance between the cylinder that make computation easyWhen one of the cylinders is resting on a surface, you can set the bar at any desired angle by simply raising the second cylinderYou obtain the desired angle when the height difference between the cylinder id equal to the sine angle multiplied by the distance between the centers of the cylinders

26 Figure 7.14The sine bar is a hypotenuse of triangle frozen in steel with a length selected to minimize computations

27 Comparison measurement with sine barsWe use gage blocks for measurement of angles with high amplification instrumentation and measure by comparisonThe sine bar is used to construct an angle equal to angle that we need to measure, but the constructed angle is in opposite direction of the actual anglePart is supported by sine barThe deviation can be detected by measuring the parallelism between the part feature and the reference surface (using dial indicator)See figure

28 Figure 7.15For comparison measurement, the sine bar is used to cancel out the angle being measured

29 Sine blocks, sine plates and sine tablesSine blocks are wide sine bar(a sine instrument wide enough to stand unsupported)Sine plates are wider sine blocks(a sine instrument rest on an integral base)Sine tables are still wider(a sine instrument is an integral part of another device, such as machine tool)

31 MECHANICAL ANGLE MEASUREMENTAnother method of angle measurement, called mechanical indexing and its related toolsThe dividing head, indexing head or index headWere developed specifically for machining rather than measurementThere are three principal classes of index headDial index headPlain index headUniversal

32 The dial index headThe lowest amplification, the dial index head is one power (1X). Therefore, it has a limited practical application today.It consist of horizontal spindle mounted on the base that rests on a reference surfaceThe plate which also an index plate, contains holes with a plunger that engages the stationary housingThe typical plate has 24 holes, which provides 360o rotation in 15o increment

35 Plain index headThe plain index head, which start at a 2X amplification, can provide a discrimination of 40X when we add worm and a gearOne third of the index plate turns of the index plate turns the spindle 9 degrees; therefore if we are using the 24-position index plate, the discrimination increases to 0o2’15”